Scilab Textbook Companion forFundamentals Of Data Structure In Cby S. Sahni , S. Anderson-freed And E.

Horowitz1

Created byAakash Yadav

B-TECHComputer Engineering

Swami Keshvanand Institute of TechnologyCollege Teacher

Richa RawalCross-Checked byLavitha Pereira

August 17, 2013

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the ”Textbook Companion Project”section at the website http://scilab.in

Book Description

Title: Fundamentals Of Data Structure In C

Author: S. Sahni , S. Anderson-freed And E. Horowitz

Publisher: University Press (India) Pvt. Ltd., New Delhi

Edition: 2

Year: 2008

ISBN: 9788173716058

1

Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

2

Contents

List of Scilab Codes 4

1 Basic concepts 6

2 Arrays and Structures 16

3 Stacks and Queues 19

4 Linked lists 31

5 Trees 44

6 Graphs 58

7 Sorting 68

8 Hashing 76

9 Priority Queues 78

3

List of Scilab Codes

Exa 1.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 6Exa 1.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 7Exa 1.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 7Exa 1.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 8Exa 1.5 example . . . . . . . . . . . . . . . . . . . . . . . . . . 8Exa 1.6 example . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exa 1.7 example . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exa 1.8 example . . . . . . . . . . . . . . . . . . . . . . . . . . 10Exa 1.9 example . . . . . . . . . . . . . . . . . . . . . . . . . . 10Exa 1.10 example . . . . . . . . . . . . . . . . . . . . . . . . . . 11Exa 1.11 example . . . . . . . . . . . . . . . . . . . . . . . . . . 12Exa 1.12 example . . . . . . . . . . . . . . . . . . . . . . . . . . 13Exa 1.13 example . . . . . . . . . . . . . . . . . . . . . . . . . . 13Exa 1.14 example . . . . . . . . . . . . . . . . . . . . . . . . . . 14Exa 1.15 example . . . . . . . . . . . . . . . . . . . . . . . . . . 14Exa 2.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 16Exa 2.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 16Exa 2.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 17Exa 1.1.b example . . . . . . . . . . . . . . . . . . . . . . . . . . 19Exa 3.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 21Exa 3.1.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 21Exa 1.2.b example . . . . . . . . . . . . . . . . . . . . . . . . . . 22Exa 3.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 24Exa 1.3.a example . . . . . . . . . . . . . . . . . . . . . . . . . . 25Exa 3.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 27Exa 4.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 31Exa 4.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 31Exa 4.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4

Exa 4.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 39Exa 5.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 44Exa 5.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 47Exa 5.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 51Exa 5.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 55Exa 6.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 58Exa 6.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 59Exa 6.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 61Exa 6.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 62Exa 6.5 example . . . . . . . . . . . . . . . . . . . . . . . . . . 63Exa 6.6 example . . . . . . . . . . . . . . . . . . . . . . . . . . 64Exa 6.7 example . . . . . . . . . . . . . . . . . . . . . . . . . . 66Exa 7.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 68Exa 7.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 69Exa 7.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . 69Exa 7.4 example . . . . . . . . . . . . . . . . . . . . . . . . . . 70Exa 7.5 example . . . . . . . . . . . . . . . . . . . . . . . . . . 71Exa 7.6 example . . . . . . . . . . . . . . . . . . . . . . . . . . 72Exa 7.7 example . . . . . . . . . . . . . . . . . . . . . . . . . . 73Exa 7.8 example . . . . . . . . . . . . . . . . . . . . . . . . . . 74Exa 8.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 76Exa 8.2 example . . . . . . . . . . . . . . . . . . . . . . . . . . 77Exa 9.1 example . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5

Chapter 1

Basic concepts

Scilab code Exa 1.1 example

1 // to do s o r t i n g o f nos . c on t a i n ed i n a l i s t2 function []= sorting(a)

3 i=1;

4 [j,k]=size(a);

5 j=i;

6 for i=1:k-1

7 for j=i:k

8 if a(i)>a(j) then

9 z=a(i);

10 a(i)=a(j);

11 a(j)=z;

12 end

13 end

14 end

15 for i=1:k

16 disp(a(i));

17 end

1819 funcprot (0);

20 endfunction

21 // c a l l i n r o u t i n e

6

22 a=[5 7 45 23 78]

23 sort=sorting(a)

Scilab code Exa 1.2 example

1 // to do b ina ry s e a r c h . .2 function []= search(a)

3 i=1;

4 [j,k]=size(a);

5 for i=1:k

6 if z==a(i) then

7 printf(”\nFOUND and index no . i s=%d\ t ”,i);

8 end

9 end

10 funcprot (0);

11 endfunction

12 // c a l l i n r o u t i n e13 a=[5 7 45 28 99]

14 z=45

15 binary=search(a)

Scilab code Exa 1.3 example

1 // to do b ina ry s e a r c h . .2 function []= search(a)

3 i=1;

4 [j,k]=size(a);

5 for i=1:k

6 if x==a(i) then

7 printf(”\nFOUND and index no . i s=%d\ t ”,i);

8 end

7

9 end

10 funcprot (0);

11 endfunction

12 // c a l l i n r o u t i n e13 a=[5 7 45 28 99]

14 x=45

15 binary=search(a)

Scilab code Exa 1.4 example

1 // example 1 . 42 // permutat ion o f a s t r i n g or c h a r a c t e r a r r ay . . .3 clear all;

4 clc;

5 x=[ ’ a ’ ’ b ’ ’ c ’ ’ d ’ ]6 printf(”\ n p o s s i b l e pe rmutat i on o f g i v en s t r i n g a r e \n

”);7 y=perms(x);

8 disp(y);

Scilab code Exa 1.5 example

1 // example 1 . 52 // ADT( Abs t ra c t Data type ) d e f i n a t i o n o f n a t u r a l

number .3 function []= ADT(x)

4 printf(”ADT na t u r a l no . i s ”);5 printf(”\nOBJECTS : an o rd e r ed subrange o f the

i n t e g e r s s t a r t i n g at z e r o and ”);6 printf(” end ing at the maximun i n t e g e r (INT MAX)

on the computer ”);7 INT_MAX =32767;

8 if x==0 // NaturalNumberZero ( )

8

9 printf(”\n” ,0);10 end

11 if x== INT_MAX then //Natura lNumberSucces sor ( x )

12 printf(”\nans . i s=%d”,x);13 else

14 printf(”\nans . i s=%d”,x+1);15 end

16 endfunction

17 // c a l l i n r o u t i n e18 x=56

19 y=ADT(x);

Scilab code Exa 1.6 example

1 // f u n c t i o n abc a c c e p t i n g on ly t h r e e s imp l e v a r i a b l e sg i v en the f u n c t i o n has

2 // on ly f i x e d s a c e r equ i r emen t . .3 function []= abc(a,b,c)

4 x= a+b+c*c+(a+b-c)/(a+b)+4.00;

5 disp(x);

6 funcprot (0);

7 endfunction

8 .... // c a l l i n g r o u t i n e9 a=[1],b=[2],c=[3]

10 abc(a,b,c)

Scilab code Exa 1.7 example

1 // To add a l i s t o f no . u s i n g a r r ay .2 function []= add(a)

3 result=sum(a);

4

9

5 printf(” a dd i t i o n o f no . on the l i s t i s=%d”,result);

6 funcprot (0);

7 endfunction

8 // c a l l i n g r o u t i n e9 a=[5 2 7 8 9 4 6]

10 r=add(a)

Scilab code Exa 1.8 example

1 clear all;

2 clc;

3 printf(”\n Example 1 . 8 ”);4 a=[2;5;4;64;78]

5 i=1;

6 x=1;............ // i n i t i a l i s i n g sum equa l s to one .7 c=1;.............. // i n i t i a l i s i n g count e qu a l s to

one .8 while i<6

9 c=c+a(i);........ //sum10 x=x+1;............... // // s t ep count11 i=i+1;

12 end

13 printf(”\n no . i n the l i s t a r e a=”)14 printf(”\n %d”,a);15 printf(”\n sum i s=%d” ,(c-1));16 printf(”\n count i s=%d” ,(x-1));

Scilab code Exa 1.9 example

1 clear all;

2 clc;

3 printf(”\n Example 1 . 9 ”);

10

4 a=[1 2 3;4 5 6];

5 b=[7 8 9;10 11 12];

6 x=matrix(a,3,2) ;........ //no . o f rows =3 ,no . o f c o l .=2.

7 y=matrix(b,3,2) ;........ //no , o f rows =3 ,no . o f c o l.=2 .

8 printf(” matr ix x=”);9 disp(x);

10 printf(” matr ix y=”);11 disp(y);

12 [p,q]=size(x);

13 i=1;

14 j=1;

15 c=1;

16 for i=1:p

17 for j=1:q

18 z(i,j)=x(i,j)+y(i,j);.......... // summing twoma t r i c e s

19 c=c+1;........... // s t e p count20 end

21 end

22 printf(”\n Re su l t an t matr ix a f t e r a d d i t i o n =”);23 disp(z);............. // d i s p l a y i n sum o f two ma t r i c e s

.24 printf(”\n s t ep count i s=%d” ,(c-1));

Scilab code Exa 1.10 example

1 clear all;

2 clc;

3 printf(”\n Example 1 . 1 0 ”);4 // f u n c t i o n to sum a l i s t o f numbers .5 function []= add()

6 printf(”\n no . i n the l i s t a r e ”);7 disp(a);

11

8 x=sum(a);

9 printf(”\n Re su l t=%d”,x);10 funcprot (0);

11 endfunction

12 // c a l l i n g r o u t i n e .13 a=[2 5 6 7 9 1 6 3 7 45]

14 add()

Scilab code Exa 1.11 example

1 clear all;

2 clc;

3 printf(”\n Example 1 . 1 1 ”);4 // Matr ix a dd i t i o n .5 a=[1 2 3;4 5 6];

6 b=[7 8 9;10 11 12];

7 x=matrix(a,3,2) ;........ //no . o f rows =3 ,no . o f c o l .=2.

8 y=matrix(b,3,2) ;........ //no , o f rows =3 ,no . o f c o l.=2 .

9 printf(” matr ix x=”);10 disp(x);

11 printf(” matr ix y=”);12 disp(y);

13 [p,q]=size(x);

14 i=1;

15 j=1;

16 for i=1:p

17 for j=1:q

18 z(i,j)=x(i,j)+y(i,j);.......... // summing twoma t r i c e s

19 end

20 end

21 printf(”\n Re su l t an t matr ix a f t e r a d d i t i o n =”);22 disp(z);............. // d i s p l a y i n sum o f two ma t r i c e s

12

.

Scilab code Exa 1.12 example

1 clear all;

2 clc;

3 printf(”Example 1 . 1 2 ”);4 // [ BIG ”oh ” ] f ( n )=O( g ( n ) ) . ( b i g oh no t a t i o n ) .5 printf(”\n \n 3n+2=O(n ) as 3n+2<=4n f o r a l l n>=2.”);6 printf(”\n \n 3n+3=O(n ) as 3n+3<=4n f o r a l l n>=3.”)

;............ // O(n ) i s c a l l e d l i n e a r .7 printf(”\n \n 3n+2=O(n ) as 100n+6<=101n f o r a l l n

>=10.”);8 printf(”\n \n 10nˆ2+4n+2=O(n ˆ2) as 10nˆ2+4n+2<=11nˆ2

f o r n>=5.”);.......... //O(n ˆ2) i s c a l l e dqu ad r a t i c .

9 printf(”\n \n 1000nˆ2+100n−6=O(n ˆ2) as 1000nˆ2+100n−6<=1001nˆ2 f o r n>=100.”);

10 printf(”\n \n 6∗2ˆn+nˆ2<=7∗2ˆn f o r n>=4”);11 printf(”\n \n 3n+3=O(n ˆ2) as 3n+3<=3nˆ2 f o r n>=2”);12 printf(”\n \n 10nˆ2+4n+2=O(n ˆ4) as 10nˆ2+4n+2<=10nˆ4

f o r n>=2.”);13 printf(”\n \n 3n+2 i s not O( 1 ) as 3n+2 i s l e s s than

or equa l to c f o r any con s t an t c and a l l n , n>=n0 .”);............ // O( 1 ) means computing t ime i sc on s t an t .

14 printf(”\n \n 10nˆ2+4n+2 i s not O( n ) ”);

Scilab code Exa 1.13 example

1 clear all;

2 clc;

3 printf(”\n Example 1 . 1 3 ”);

13

4 printf(”\n \n [ Omega ] f ( n )=omega ( g ( n ) ) ”);5 printf(”\n \n 3n+2=omega ( n ) as 3n+2>=3n f o r n>=1”);6 printf(”\n \n 3n+3=omega ( n ) as 3n+3>=3n f o r n>=1”);7 printf(”\n \n 100n+6=omega ( n ) as 100n+6>=100n f o r n

>=1”);8 printf(”\n \n 10nˆ2+4n+2=omega ( n ˆ2) as 10nˆ2+4n+2>=n

ˆ2 f o r n>=1”);9 printf(”\n \n 6∗2ˆn+nˆ2=omega ( n ) as 6∗2ˆn+nˆ2>=2ˆn

f o r n>=1”);10 printf(”\n \n 3n+3=omega ( 1 ) ”);11 printf(” \n \n \ t [ Omega ] f ( n )=omega ( 1 ) ”);

Scilab code Exa 1.14 example

1 clear all;

2 clc;

3 printf(”\n Example 1 . 1 4 ”);4 printf(”\n \n [ Theta ] f ( n )=th e t a ( g ( n ) ) ”);5 printf(”\n \n 3n+2=the t a ( n ) as 3n+2>=3n f o r a l n>=2

”);6 printf(”\n \n 3n+3=the t a ( n ) ”);7 printf(”\n \n 10nˆ2+4n+2=the t a ( n ˆ2) ”);8 printf(”\n \n 6∗2ˆn+nˆ2= the t a (2ˆ n ) ”);9 printf(”\n \n 3n+2 i s not t h e t a ( 1 ) ”);

10 printf(”\n \n 3n+3 i s not t h e t a ( n ˆ2) \n”);11 printf(”\n \n The Theta n o t a t i o n i s more p r e c i s e

than both b i g oh and omega no ta i on ”);

Scilab code Exa 1.15 example

1 clear all;

2 clc;

3 printf(”\n \ t Example 1 . 1 5 ”);

14

4 // how va r i o u s f u n c t i o n s grow with n , p l o t t i n g o fv a r i o u s f u n c t i o n s i s b e ing shown .

5 // l i k e f u n c t i o n 2ˆn grows very r a p i d l y with n . andu t i l i t y o f programs with e x p on e n t i a l c omp l ex i t yi s l i m i t e d to sma l l n ( t y p i c a l l y n<=40) .

6 n=[ 1 2 3 4 5 6];....... // t a k i n va lu e o f n from 1to 10 to ob s e r v e the v a r i a t i o n i n v a r i o u sf u n c t i o n s .

7 plot(log (n));

8 plot (2^n);

9 plot(n);

10 plot(n^2);

11 xtitle(” P lo t o f f u n c t i o n v a l u e s ”,”n −−>”,” f −−>”);12 printf(” \n \n X − a x i s i s r e p r e s e n t e d by v a l u e s o f

n and Y−a x i s i f r e p r e s e n t e d by f ”);

15

Chapter 2

Arrays and Structures

Scilab code Exa 2.1 example

1 clear all;

2 clc;

3 printf(”\n example 2 . 1 ”);4 // p r i n t i n g out v a l u e s o f the a r r ay .5 a=[31 40 57 46 97 84];

6 printf(”\ nva l u e s a r e : \ n”);7 disp(a);

Scilab code Exa 2.2 example

1 clear all;

2 clc;

3 printf(”\n Example 2 . 2\ n”);4 // S t r i n g i n s e r t i o n .5 s=” auto ” ;............... // 1 s t s t r i n g or c h a r a c t e r

a r r ay .6 x=” mob i l e ” ;............... // 2nd s t r i n g or c h a r a c t e r

a r r ay .

16

7 z=s+x;.......... // c on c a t e n a t i o n o f 2 s t r i n g s .8 printf(”\ t s t r i n g s=”);9 disp(s);

10 printf(”\ t s t r i n g x=”);11 disp(x);

12 printf(”\ t c on c a t ena t ed s t r i n g z=”);13 disp(z);........ // d i s p a l y i n g conca t ena t ed s t r i n g .

Scilab code Exa 2.3 example

1 clear all;

2 clc;

3 printf(”\nExample 2 . 3\ n”);4 // compa r i s i on o f 2 s t r i n g s .5 a=”hakunah” ;.......... // s t r i n g 1 .6 b=”matata ” ;............. // s t r i n g 2 .7 disp(” a & b r e s p e c t i v e l y a r e =”);8 disp(a);

9 disp(b);

10 disp(” comparing s t r i n g s ”);11 z=strcmp(a,b);......... // compa r i s i on o f 2 s t r i n g s .12 if(z==0)

13 printf(”\nMATCHED\n”);....... // i f s t r i n g smatched strcmp r e t u r n s 0 .

14 else

15 printf(”\nNOT MATCHED\n”);......... // i f s t r i n gdoesn ’ t matched strcmp r e t u r n s −1.

16 end

17 q=” akash ”;18 w=” akash ”;19 disp(”q & w r e s p e c t i v e l y a r e=”);20 disp(q);

21 disp(w);

22 disp(” comparing s t r i n g s ”);23 x=strcmp(q,w);

17

24 if(x==0)

25 printf(”\nMATCHED\n”);....... // i f s t r i n g smatched strcmp r e t u r n s 0 .

26 else

27 printf(”\nNOT MATCHED\n”);......... // i f s t r i n gdoesn ’ t matched strcmp r e t u r n s −1.

28 end

18

Chapter 3

Stacks and Queues

Scilab code Exa 1.1.b example

1 // Ex e r c i s e q u e s t i o n 2 :2 // Implement ing Push And Pop Func t i on s :3 function[y,sta1]= empty(sta)

4 y=0;

5 sta1 =0;

6 if(sta.top ==0)

7 y=0;

8 else

9 y=1;

10 end

11 sta1=sta

12 endfunction

1314 function[sta]=push(stac ,ele)

15 sta =0;

16 if(empty(stac)==0)

17 stac.a=ele;

18 stac.top=stac.top+1;

19 else

20 stac.a=[stac.a(:,:) ele]

21 stac.top=stac.top+1;

19

22 end

23 disp(stac);

24 sta=stac;

25 funcprot (0)

26 endfunction

2728 function[ele ,sta]=pop(stack)

29 ele= ’−1 ’ ;30 if(empty(stack)==0)

31 disp(” Stack Under f low ”);32 break;

33 else

34 ele=stack.a(stack.top);

35 stack.top=stack.top -1;

36 if(stack.top ~=0)

37 b=stack.a(1);

38 for i2=2: stack.top

39 b=[b(:,:) stack.a(i2)];

40 end

41 stack.a=b;

42 else

43 stack.a= ’ 0 ’ ;44 end

45 end

46 disp(stack);

47 sta=stack;

48 endfunction

49 global stack

50 // Ca l l i n g Rout ine :51 stack=struct( ’ a ’ ,0, ’ top ’ ,0);52 stack=push(stack ,4);

53 stack=push(stack ,55);

54 stack=push(stack ,199);

55 stack=push(stack ,363);

56 [ele ,stack]=pop(stack);

57 disp(stack ,” A f t e r the above o p e r a t i o n s s t a c k i s : ”);

20

Scilab code Exa 3.1 example

1 clear all;

2 clc;

3 printf(”\nexample 3 . 1\ n”);4 // s t a c k s f o l l o w LIFO i . e l a s t i n f i r s t out . so

p r i n t i n g out a r r ay from l a s t to f i r s t w i l l besame as s t a c k .

5 a=[12;35;16;48;29;17;13]

6 i=7;

7 printf(”\ t s t a c k =”);8 while i>0

9 printf(”\n\t%d”,a(i));10 i=i-1;

11 end

Scilab code Exa 3.1.2 example

1 // Unolved Example 2 :2 clear all;

3 clc;

4 disp(” Unsolved example 2”);5 // Implement ing Stack u s i ng union :6 function[stack ]= sta_union(etype ,a)

7 stackelement=struct( ’ e type ’ ,etype);8 [k,l]=size(a);

9 select stackelement.etype ,

10 case ’ i n t ’ then

11 a=int32(a);

12 stack=struct( ’ top ’ ,l, ’ i t ems ’ ,a);,13 case ’ f l o a t ’ then

14 a=double(a);

21

15 stack=struct( ’ top ’ ,l, ’ i t ems ’ ,a);,16 case ’ char ’ then

17 a=string(a);

18 stack=struct( ’ top ’ ,l, ’ i t ems ’ ,a);,19 end

20 disp(stack ,” Stack i s : ”);21 endfunction

22 a=[32 12.34 232 32.322]

23 stack=sta_union( ’ f l o a t ’ ,a)24 stack=sta_union( ’ i n t ’ ,a)25 stack=sta_union( ’ char ’ ,a)

Scilab code Exa 1.2.b example

1 // Unsolved Example 12 clear all;

3 clc;

4 disp(” example 3 . 7 ”);5 //To de t e rmine the s y n t a c t i c a l y v a l i d s t r i n g6 function[l]= strlen(x)

7 i=1;

8 l=0;

9 [j,k]=size(x)

10 for i=1:k

11 l=l+length(x(i));

12 end

13 endfunction

14 function []= stringvalid(str)

15 str=string(str);

16 stack=struct( ’ a ’ , ’ 0 ’ , ’ top ’ ,0);17 l1=strlen(str);

18 valid =1;

19 l=1;

20 while(l<=l1)

21 if(str(l)== ’ ( ’ |str(l)== ’ [ ’ |str(l)== ’ { ’ )

22

22 if(stack.top ==0)

23 stack.a=str(l);

24 stack.top=stack.top +1;

25 else

26 stack.a=[stack.a(:,:) str(l)];

27 stack.top=stack.top +1;

28 end

29 disp(stack);

30 end

31 if(str(l)== ’ ) ’ |str(l)== ’ ] ’ |str(l)== ’ } ’ )32 if(stack.top ==0)

33 valid =0;

34 break;

35 else

36 i=stack.a(stack.top);

37 b=stack.a(1);

38 for i1=2: stack.top -1

39 b=[b(:,:) stack.a(i1)]

40 end

41 stack.a=b;

42 stack.top=stack.top -1;

43 symb=str(l);

44 disp(stack);

45 if((( symb== ’ ) ’ )&(i== ’ ( ’ ))|(( symb== ’ ] ’ )&(i==’ [ ’ ))|(( symb== ’ } ’ )&(i== ’ { ’ )))

46 else

47 valid =0;

48 break;

49 end

50 end

51 end

52 l=l+1;

53 end

54 if(stack.top ~=0)

55 valid =0;

56 end

57 if(valid ==0)

58 disp(” I n v a l i d S t r i n g ”);

23

59 else

60 disp(” Va l id S t r i n g ”);61 end

62 endfunction

63 // Ca l l i n g Rout ine :64 stringvalid ([ ’ ( ’ ’A ’ ’+ ’ ’B ’ ’ } ’ ’ ) ’ ])65 stringvalid ([ ’ { ’ ’ [ ’ ’A ’ ’+ ’ ’B ’ ’ ] ’ ’− ’ ’ [ ’ ’ ( ’

’C ’ ’− ’ ’D ’ ’ ) ’ ’ ] ’ ])66 stringvalid ([ ’ ( ’ ’A ’ ’+ ’ ’B ’ ’ ) ’ ’− ’ ’ { ’ ’C ’ ’+ ’ ’

D ’ ’ } ’ ’− ’ ’ [ ’ ’F ’ ’+ ’ ’G ’ ’ ] ’ ])67 stringvalid ([ ’ ( ’ ’ ( ’ ’H ’ ’ ) ’ ’ ∗ ’ ’ { ’ ’ ( ’ ’ [ ’ ’ J ’ ’

+ ’ ’K ’ ’ ] ’ ’ ) ’ ’ } ’ ’ ) ’ ])68 stringvalid ([ ’ ( ’ ’ ( ’ ’ ( ’ ’A ’ ’ ) ’ ’ ) ’ ’ ) ’ ])

Scilab code Exa 3.2 example

1 // example 3 . 22 //Queue Ope ra t i on s3 clear all;

4 clc;

5 function[q2]=push(ele ,q1)

6 if(q1.rear==q1.front)

7 q1.a=ele;

8 q1.rear=q1.rear +1;

9 else

10 q1.a=[q1.a(:,:) ele];

11 q1.rear=q1.rear +1;

12 end

13 q2=q1;

14 endfunction

15 funcprot (0);

16 function[ele ,q2]=pop(q1)

17 ele=-1;

18 q2=0;

19 if(q1.rear==q1.front)

24

20 disp(”Queue Under f low ”);21 return;

22 else

23 ele=q1.a(q1.rear -q1.front);

24 q1.front=q1.front +1;

25 i=1;

26 a=q1.a(1);

27 for i=2:(q1.rear -q1.front)

28 a=[a(:,:) q1.a(i)];

29 end

30 q1.a=a;

31 end

32 q2=q1;

33 endfunction

34 funcprot (0);

35 // Ca l l i n g Rout ine :36 q1=struct( ’ a ’ ,0, ’ r e a r ’ ,0, ’ f r o n t ’ ,0)37 q1=push(3,q1)

38 q1=push(22,q1);

39 q1=push(21,q1);

40 disp(q1,”Queue a f t e r i n s e r t i o n ”);41 [ele ,q1]=pop(q1)

42 disp(ele ,”poped e l ement ”);43 disp(q1,”Queue a f t e r poping ”);44 [ele ,q1]=pop(q1);

45 [ele ,q1]=pop(q1);

46 [ele ,q1]=pop(q1);// Under f low Cond i t i on

Scilab code Exa 1.3.a example

1 clear all;

2 clc;

3 disp(” Unsolved example 3”);4 function[l]= strlen(x)

5 i=1;

25

6 l=0;

7 [j,k]=size(x)

8 for i=1:k

9 l=l+length(x(i));

10 end

11 endfunction

12 function []= str(st)

13 stack=struct( ’ a ’ ,0, ’ top ’ ,0);14 st=string(st);

15 l=1;

16 l1=strlen(st);

17 symb=st(l);

18 valid =1;

19 while(l<l1)

20 while(symb~= ’C ’ )21 if(stack.top ==0)

22 stack.a=st(l);

23 stack.top=stack.top +1;

24 else

25 stack.a=[stack.a(:,:) st(l)];

26 stack.top=stack.top +1;

27 end

28 l=l+1;

29 symb=st(l);

30 end

31 i=st(l+1);

32 if(stack.top ==0)

33 valid =0;

34 break;

35 else

36 symb1=stack.a(stack.top);

37 stack.top=stack.top -1;

38 if(i~= symb1)

39 valid =0;

40 break;

41 end

42 end

43 l=l+1;

26

44 end

45 if(stack.top ~=0)

46 valid =0;

47 end

48 if(valid ==0)

49 disp(”Not o f the g i v en format ”);50 else

51 disp(” S t r i n g Of the Given Format”);52 end

53 endfunction

54 // Ca l l i n g Rout ine :55 st=[ ’A ’ ’A ’ ’B ’ ’A ’ ’C ’ ’A ’ ’B ’ ’A ’ ’A ’ ]56 str(st)

57 st=[ ’A ’ ’A ’ ’B ’ ’A ’ ’C ’ ’A ’ ’B ’ ’A ’ ]

58 str(st)

Scilab code Exa 3.3 example

1 // So lved Example 3 . 3 :2 // Conver ing an i n f i x e x p r e s s i o n to a P o s t f i x

Exp r e s s i on :3 function[sta]=push(stac ,ele)

4 sta =0;

5 if(stac.top ==0)

6 stac.a=ele;

7 stac.top=stac.top+1;

8 else

9 stac.a=[stac.a(:,:) ele]

10 stac.top=stac.top+1;

11 end

12 disp(stac);

13 sta=stac;

14 endfunction

1516 function[ele ,sta]=pop(stack)

27

17 ele= ’−1 ’ ;18 if(stack.top ==0)

19 disp(” Stack Under f low ”);20 break;

21 else

22 ele=stack.a(stack.top);

23 stack.top=stack.top -1;

24 if(stack.top ~=0)

25 b=stack.a(1);

26 for i2=2: stack.top

27 b=[b(:,:) stack.a(i2)];

28 end

29 stack.a=b;

30 else

31 stack.a= ’ 0 ’ ;32 end

33 end

34 sta=stack;

35 endfunction

36 function[l]= strlen(x)

37 i=1;

38 l=0;

39 [j,k]=size(x)

40 for i=1:k

41 l=l+length(x(i));

42 end

43 endfunction

44 function[p]=pre(s1,s2)

45 i1=0;

46 select s1,

47 case ’+ ’ then i1=5;

48 case ’− ’ then i1=5;

49 case ’ ∗ ’ then i1=9;

50 case ’ / ’ then i1=9;

51 end

52 i2=0;

53 select s2,

54 case ’+ ’ then i2=5;

28

55 case ’− ’ then i2=5;

56 case ’ ∗ ’ then i2=9;

57 case ’ / ’ then i2=9;

58 end

59 p=0;

60 p=i1 -i2;

61 if(s1== ’ ( ’ )62 p=-1;

63 end

64 if(s2== ’ ( ’ &s1~= ’ ) ’ )65 p=-1;

66 end

67 if(s1~= ’ ( ’ &s2== ’ ) ’ )68 p=1;

69 end

7071 endfunction

72 function[a2]= intopo(a1,n)

73 stack=struct( ’ a ’ ,0, ’ top ’ ,0);74 l1=1;

75 l2=strlen(a1(1))

76 for i=2:n

77 l2=l2+strlen(a1(i))

78 end

79 a2=list();

80 while(l1 <=l2)

81 symb=a1(l1);

82 if(isalphanum(string(a1(l1))))

83 a2=list(a2,symb);

84 else

85 while(stack.top ~=0&( pre(stack.a(stack.top),

symb) >=0))

86 [topsymb ,stack ]=pop(stack);

87 if(topsymb == ’ ) ’ |topsymb == ’ ( ’ )88 a2=a2;

89 else

90 a2=list(a2 ,topsymb);

91 end

29

92 end

93 if(stack.top ==0| symb~= ’ ) ’ )94 stack=push(stack ,symb);

95 else

96 [ele ,stack]=pop(stack);

97 end

98 end

99 l1=l1+1;

100 end

101 while(stack.top ~=0)

102 [topsymb ,stack ]=pop(stack);

103 if(topsymb == ’ ) ’ |topsymb == ’ ( ’ )104 a2=a2;

105 else

106 a2=list(a2,topsymb);

107 end

108 end

109 disp(a2);

110 endfunction

111 // Ca l l i n g Rout ine :112 a1=[ ’ ( ’ ’ 2 ’ ’+ ’ ’ 3 ’ ’ ) ’ ’ ∗ ’ ’ ( ’ ’ 5 ’ ’− ’ ’ 4 ’ ’ ) ’ ]113 a2=intopo(a1 ,11)

30

Chapter 4

Linked lists

Scilab code Exa 4.1 example

1 // L i s t o f words i n a l i n k e d l i s t .2 clear all;

3 clc;

4 printf(”\n Exapmle 4 . 1\ n”);5 x=list( ’ s c i ’ , ’ l ab ’ , ’ t e x t ’ , ’ companionsh ip ’ , ’ p r o j e c t ’ )

;

6 disp(”x=”);7 disp(x);

Scilab code Exa 4.2 example

1 //CIRCULAR LINKED LIST2 clear all;

3 clc;

4 funcprot (0);

5 disp(”Example 4 . 2 ”);6 function[link2 ]= append(ele ,link1)

7 link2=list

31

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

8 if(link1 (1) (1).add ==0)

9 link1 (1) (1).data=ele;

10 link1 (1) (1).add=1;

11 link1 (1) (1).nexadd =1;

12 link2 (1)=link1 (1) (1);

13 else

14 if(link1 (1) (1).nexadd ==link1 (1) (1).add)

15 lin2=link1 (1) (1);

16 lin2.data=ele;

17 lin2.add=link1 (1)(1).add +1;

18 link1 (1) (1).nexadd=lin2.add;

19 lin2.nexadd=link1 (1)(1).add;

20 link2 (1)=link1 (1) (1);

21 link2 (2)=lin2;

22 else

23 lin2=link1 (1) (1);

24 i=1;

25 while(link1(i)(1).nexadd ~= link1 (1)(1).add)

26 i=i+1;

27 end

28 j=i;

29 lin2.data=ele;

30 lin2.add=link1(i).add+1;

31 lin2.nexadd=link1 (1)(1).add;

32 link1(i).nexadd=lin2.add;

33 link2 (1)=link1 (1) (1);

34 i=2;

35 while(link1(i).nexadd ~=lin2.add)

36 link2(i)=(link1(i));

37 i=i+1;

38 end

39 link2(i)=link1(i);

40 link2(i+1)=lin2;

41 end

42 end

43 endfunction

32

44 function[link2 ]=add(ele ,pos ,link1);

45 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

46 i=1;

47 while(i<=pos)

48 if(link1(i).nexadd ==link1 (1)(1).add)

49 break;

50 else

51 i=i+1;

52 end

53 end

54 if(link1(i).nexadd ~=link1 (1)(1).add)

55 i=i-1;

56 lin2.data=ele;

57 lin2.add=i;

58 j=i;

59 while(link1(j).nexadd ~= link1 (1)(1).add)

60 link1(j).add=link1(j).add+1;

61 link1(j).nexadd=link1(j).nexadd +1;

62 j=j+1;

63 end

64 link1(j).add=link1(j).add+1;

65 lin2.nexadd=link1(i).add;

66 link1(i-1).nexadd=lin2.add;

67 k=1;

68 while(k<i)

69 link2(k)=link1(k);

70 k=k+1;

71 end

72 link2(k)=lin2;

73 k=k+1;

74 link2(k)=link1(k-1);

75 k=k+1

76 l=k-1;

77 while(k~=j)

78 link2(k)=link1(l);

79 k=k+1;

33

80 l=l+1;

81 end

82 link2(j)=link1(j-1);;

83 link2(j+1)=link1(j);

84 else

85 if(i==pos)

86 k=1;

87 lin2.data=ele;

88 lin2.add=link1(i-1).add +1;

89 link1(i).add=link1(i).add+1;

90 lin2.nexadd=link1(i).add;

91 link1(i).nexadd=link1 (1)(1).add;

92 k=1;

93 while(k<pos)

94 link2(k)=link1(k);

95 k=k+1;

96 end

97 link2(k)=lin2;

98 link2(k+1)=link1(k)

99 end

100 end

101102 endfunction

103 function[link2 ]= delete1(pos ,link1)

104 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

105 i=1;

106 j=1;

107 while(i<pos)

108 if(( link1(j).nexadd ==link1 (1) (1).add))

109 j=1;

110 i=i+1;

111 else

112 i=i+1;

113 j=j+1;

114 end

115 end

34

116 if(link1(j).nexadd ~=link1 (1)(1).add)

117 k=1;

118 if(j==1)

119 k=2;

120 while(link1(k).nexadd ~= link1 (1)(1).add)

121 link2(k-1)=link1(k);

122 k=k+1;

123 end

124 link2(k-1)=link1(k);

125 link2(k-1).nexadd=link2 (1).add;

126 else

127 lin2=link1(j);

128 link1(j-1).nexadd=link1(j+1).add;

129 k=1;

130 while(link1(k).nexadd ~= link1(j+1).add)

131 link2(k)=link1(k);

132 k=k+1;

133 end

134 link2(k)=link1(k);

135 k=k+2;

136 while(link1(k).nexadd ~= link1 (1)(1).add)

137 link2(k-1)=link1(k);

138 k=k+1;

139 end

140 link2(k-1)=link1(k);

141 end

142 else

143 link1(j-1).nexadd=link1 (1)(1).add;

144 l=1;

145 while(link1(l).nexadd ~= link1 (1)(1).add)

146 link2(l)=link1(l);

147 l=l+1;

148 end

149 link2(l)=link1(l);

150 end

151 endfunction

152 // Ca l l i n g Rout ine :153 link1=struct( ’ data ’ ,0, ’ add ’ ,0, ’ nexadd ’ ,0);

35

154 link1=append(4,link1);// This w i l l a c t u a l y c r e a t e al i s t and 4 as s t a r t

155 link1=append(6,link1);

156 link1=add(10,2, link1);

157 link1=delete1(4,link1);//As the l i s t i s c i r c u l a r the4 ’ th e l ement r e f e r s to a c t u a l y the 1 ’ s t one

158 disp(link1 ,” A f t e r the above manup la t i ons the l i s t i s”);

Scilab code Exa 4.3 example

1 // L i s t I n s e r t i o n .2 clc;

3 clear all;

4 disp(”Example 4 . 3 ”);5 funcprot (0)

6 function[link2 ]= insert_pri(ele ,link1)

7 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

8 if(link1 (1) (1).add ==0)

9 link1 (1) (1).data=ele;

10 link1 (1) (1).add=1;

11 link1 (1) (1).nexadd =1;

12 link2 (1)=link1 (1) (1);

13 else

14 if(link1 (1) (1).nexadd ==link1 (1) (1).add)

15 if(ele >=link1 (1)(1).data)

16 t=ele;

17 p=link1 (1) (1).data;

18 else

19 t=link1 (1) (1).data;

20 p=ele;

21 end

22 link1 (1) (1).data=t;

36

23 lin2=link1 (1) (1);

24 lin2.data=p;

25 lin2.add=2;

26 lin2.nexadd=link1 (1)(1).add;

27 link1 (1) (1).nexadd=lin2.add;

28 link2 (1)=link1 (1) (1);

29 link2 (2)=lin2;

30 else

31 i=1;

32 a=[];

33 while(link1(i).nexadd ~= link1 (1)(1).add)

34 a=[a(:,:) link1(i).data];

35 i=i+1;

36 end

37 a=[a(:,:) link1(i).data];

38 a=gsort(a);

39 j=1;

40 while(j<=i)

41 link1(j).data=a(j);

42 j=j+1;

43 end

44 k=1;

45 while(link1(k).data >=ele)

46 if(link1(k).nexadd ==link1 (1)(1).add)

47 break;

48 else

49 link2(k)=link1(k);

50 k=k+1;

51 end

52 end

53 if(link1(k).nexadd ~=link1 (1)(1).add)

54 lin2=link1(k);

55 lin2.data=ele;

56 lin2.add=link1(k).add;

57 j=k;

58 y=link1 (1) (1).add;

59 while(link1(k).nexadd ~=y)

60 link1(k).add=link1(k).add+1;

37

61 link1(k).nexadd=link1(k).nexadd +1;

62 k=k+1;

63 end

64 link1(k).add=link1(k).add+1;

65 lin2.nexadd=link1(j).add;

66 link2(j)=lin2;

67 j=j+1;

68 while(j<=k+1)

69 link2(j)=link1(j-1);

70 j=j+1;

71 end

72 else

73 lin2=link1(k);

74 lin2.data=ele;

75 lin2.nexadd=link1 (1)(1).add;

76 lin2.add=link1(k).add+1;

77 link1(k).nexadd=lin2.add;

78 j=1;

79 while(j<=k)

80 link2(j)=link1(j);

81 j=j+1;

82 end

83 link2(j)=lin2;

84 end

85 end

86 end

87 endfunction

88 // Ca l l i n g Rout ine :89 link1=struct( ’ data ’ ,0, ’ add ’ ,0, ’ nexadd ’ ,0);90 link1=insert_pri (3,link1);

91 link1=insert_pri (4,link1);

92 link1=insert_pri (22,link1);

93 link1=insert_pri (21,link1);

94 link1=insert_pri (11,link1);

95 disp(link1 ,” L i s t A f t e r I n s e r t i o n s ”);

38

Scilab code Exa 4.4 example

1 // De l e t i o n from the l i s t :2 function[link2 ]= append(ele ,link1)

3 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

4 if(link1 (1) (1).add ==0)

5 link1 (1) (1).data=ele;

6 link1 (1) (1).add=1;

7 link1 (1) (1).nexadd =0;

8 link1 (1) (1).prevadd =0;

9 link2 (1)=link1 (1) (1);

10 else

11 if(link1 (1) (1).nexadd ==0)

12 lin2=link1 (1) (1);

13 lin2.data=ele;

14 lin2.add=link1 (1)(1).add +1;

15 link1 (1) (1).nexadd=lin2.add;

16 lin2.nexadd =0;

17 lin2.prevadd=link1 (1) (1).add;

18 link2 (1)=link1 (1) (1);

19 link2 (2)=lin2;

20 else

21 lin2=link1 (1) (1);

22 i=1;

23 while(link1(i)(1).nexadd ~=0)

24 i=i+1;

25 end

26 j=i;

27 lin2.data=ele;

28 lin2.add=link1(i).add +1;

29 lin2.nexadd =0;

30 link1(i).nexadd=lin2.add;

39

31 lin2.prevadd=link1(i).add;

32 link2 (1)=link1 (1) (1);

33 i=2;

34 while(link1(i).nexadd ~=lin2.add)

35 link2(i)=(link1(i));

36 i=i+1;

37 end

38 link2(i)=link1(i);

39 link2(i+1)=lin2;

40 end

41 end

42 endfunction

43 function[link2 ]=add(ele ,pos ,link1);

44 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

45 i=1;

46 while(i<=pos)

47 if(link1(i).nexadd ==0)

48 break;

49 else

50 i=i+1;

51 end

52 end

53 if(link1(i).nexadd ~=0)

54 i=i-1;

55 lin2.data=ele;

56 lin2.add=i;

57 j=i;

58 while(link1(j).nexadd ~=0)

59 link1(j).prevadd=link1(j).prevadd +1;

60 link1(j).add=link1(j).add+1;

61 link1(j).nexadd=link1(j).nexadd +1;

62 j=j+1;

63 end

64 link1(j).prevadd=link1(j).prevadd +1;

65 link1(j).add=link1(j).add+1;

66 lin2.nexadd=link1(i).add;

40

67 link1(i).prevadd=lin2.add;

68 lin2.prevadd=link1(i-1).add;

69 link1(i-1).nexadd=lin2.add;

70 k=1;

71 while(k<i)

72 link2(k)=link1(k);

73 k=k+1;

74 end

75 link2(k)=lin2;

76 k=k+1;

77 link2(k)=link1(k-1);

78 k=k+1

79 l=k-1;

80 while(k~=j)

81 link2(k)=link1(l);

82 k=k+1;

83 l=l+1;

84 end

85 link2(j)=link1(j-1);;

86 link2(j+1)=link1(j);

87 else

88 if(i==pos)

89 k=1;

90 lin2.data=ele;

91 lin2.add=link1(i-1).add +1;

92 link1(i).add=link1(i).add+1;

93 lin2.nexadd=link1(i).add;

94 link1(i).prevadd=lin2.add;

95 lin2.prevadd=link1(i-1).add;

96 k=1;

97 while(k<pos)

98 link2(k)=link1(k);

99 k=k+1;

100 end

101 link2(k)=lin2;

102 link2(k+1)=link1(k)

103 end

104 end

41

105106 endfunction

107 function[link2 ]= delete1(pos ,link1)

108 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

109 i=1;

110 while(i<=pos)

111 if(( link1(i).nexadd ==0))

112 break;

113 else

114 i=i+1;

115 end

116 end

117 if(link1(i).nexadd ~=0)

118 i=i-1;

119 j=1;

120 if(i==1)

121 j=1;

122 while(link1(j).nexadd ~=0)

123 link2(j)=link1(j);

124 j=j+1;

125 end

126 link2(j)=link1(j);

127 else

128 link1(i-1).nexadd=link1(i+1).add;

129 link1(i+1).prevadd=link1(i-1).add;

130 while(link1(j).nexadd ~= link1(i+1).add)

131 link2(j)=link1(j);

132 j=j+1;

133 end

134 if(j~=i-1)

135 link2(j)=link1(j);

136 link2(j+1)=link1(j+1);

137 k=i+1;

138 l=2;

139 else

140 link2(j)=link1(j);

42

141 k=i+1;

142 l=1;

143 end

144 while(link1(k).nexadd ~=0)

145 link2(j+l)=link1(k);

146 k=k+1;

147 l=l+1;

148 end

149 link2(j+l)=link1(k);

150 end

151 else

152 if(i==pos)

153 j=1;

154 link1(i-1).nexadd =0;

155 while(j<=i-1)

156 link2(j)=link1(j);

157 j=j+1;

158 end

159 end

160 end

161 endfunction

162 // Ca l l i n g Rout ine :163 link1=struct( ’ data ’ ,0, ’ add ’ ,0, ’ nexadd ’ ,0);164 link1=append(4,link1);

165 link1=append(6,link1);

166 link1=add(10,2, link1);

167 link1=delete1(3,link1);

168 disp(link1 ,” A f t e r the above man ipu l a t i on the l i s t i s”);

43

Chapter 5

Trees

Scilab code Exa 5.1 example

12 funcprot (0);

3 function[tree]= maketree(x)

4 tree=zeros (30 ,1);

5 for i=1:30

6 tree(i)=-1;

7 end

8 tree (1)=x;

9 tree (2)=-2;

10 endfunction

11 function[tree1 ]= setleft(tree ,tre ,x)

12 tree1 =[];

13 i=1;

14 while(tree(i)~=-2)

15 if(tree(i)==tre)

16 j=i;

17 end

18 i=i+1;

19 end

20 if(i>2*j)

21 tree (2*j)=x;

44

22 else

23 tree (2*j)=x;

24 tree (2*j+1)=-2;

25 for l=i:2*j-1

26 tree(i)=-1;

27 end

28 end

29 tree1=tree;

30 endfunction

31 function[tree1 ]= setright(tree ,tre ,x)

32 tree1 =[];

33 i=1;

34 while(tree(i)~=-2)

35 if(tree(i)==tre)

36 j=i;

37 end

38 i=i+1;

39 end

40 if(i>2*j+1)

41 tree (2*j+1)=x;

42 else

43 tree (2*j+1)=x;

44 tree (2*j+2)=-2;

45 for l=i:2*j

46 tree(i)=-1;

47 end

48 end

49 tree1=tree;

50 endfunction

51 function[x]= isleft(tree ,tre)

52 i=1;

53 x=0;

54 while(tree(i)~=-2)

55 if(tree(i)==tre)

56 j=i;

57 end

58 i=i+1;

59 end

45

60 if(i>=2*j)

61 if((tree (2*j)~=-1)|(tree (2*j)~=-2))

62 x=1;

63 return 1;

64 else

65 return 0;

66 end

67 else

68 x=0;

69 return x;

70 end

71 endfunction

72 function[x]= isright(tree ,tre)

73 i=1;

74 x=0;

75 while(tree(i)~=-2)

76 if(tree(i)==tre)

77 j=i;

78 end

79 i=i+1;

80 end

81 if(i>=2*j+1)

82 if((tree (2*j+1)~=-1)|(tree (2*j+1)~=-2))

83 x=1;

84 return 1;

85 else

86 return 0;

87 end

88 else

89 x=0;

90 return x;

91 end

92 endfunction

93 // Ca l l i n g Rout ine :94 tree=maketree (3);

95 disp(tree ,” Tree made”);96 tree=setleft(tree ,3,1);

97 disp(tree ,” A f t e r s e t t i n g 1 to l e f t o f 3”);

46

98 tree=setright(tree ,3,2);

99 disp(tree ,” A f t e r s e t t i n g 2 to r i g h t o f 3”);100 tree=setright(tree ,2,4);

101 tree=setleft(tree ,2,5);

102 tree=setright(tree ,1,6);

103 tree=setright(tree ,5,8);

104 disp(tree ,” A f t e r above o p e r a t i o n s : ”);105 x=isright(tree ,3);

106 disp(x,” Checking f o r the r i g h t son o f 3 ye s i f 1e l s e no”);

107 x=isleft(tree ,2);

108 disp(x,”Check f o r l e f t son o f 2”);

Scilab code Exa 5.2 example

1 funcprot (0);

2 function[tree]= maketree(x)

3 tree=zeros (30 ,1);

4 for i=1:30

5 tree(i)=-1;

6 end

7 tree (1)=x;

8 tree (2)=-2;

9 endfunction

10 function[tree1 ]= setleft(tree ,tre ,x)

11 tree1 =[];

12 i=1;

13 while(tree(i)~=-2)

14 if(tree(i)==tre)

15 j=i;

16 end

17 i=i+1;

18 end

19 if(i>2*j)

20 tree (2*j)=x;

47

21 else

22 tree (2*j)=x;

23 tree (2*j+1)=-2;

24 for l=i:2*j-1

25 tree(i)=-1;

26 end

27 end

28 tree1=tree;

29 endfunction

30 function[tree1 ]= setright(tree ,tre ,x)

31 tree1 =[];

32 i=1;

33 while(tree(i)~=-2)

34 if(tree(i)==tre)

35 j=i;

36 end

37 i=i+1;

38 end

39 if(i>2*j+1)

40 tree (2*j+1)=x;

41 else

42 tree (2*j+1)=x;

43 tree (2*j+2)=-2;

44 for l=i:2*j

45 tree(i)=-1;

46 end

47 end

48 tree1=tree;

49 endfunction

50 function[x]= isleft(tree ,tre)

51 i=1;

52 x=0;

53 while(tree(i)~=-2)

54 if(tree(i)==tre)

55 j=i;

56 end

57 i=i+1;

58 end

48

59 if(i>=2*j)

60 if((tree (2*j)~=-1)|(tree (2*j)~=-2))

61 x=1;

62 return 1;

63 else

64 return 0;

65 end

66 else

67 x=0;

68 return x;

69 end

70 endfunction

71 function[x]= isright(tree ,tre)

72 i=1;

73 x=0;

74 while(tree(i)~=-2)

75 if(tree(i)==tre)

76 j=i;

77 end

78 i=i+1;

79 end

80 if(i>=2*j+1)

81 if((tree (2*j+1)~=-1)|(tree (2*j+1)~=-2))

82 x=1;

83 return 1;

84 else

85 return 0;

86 end

87 else

88 x=0;

89 return x;

90 end

91 endfunction

92 funcprot (0);

93 function []= inorder(tree ,p)

94 if(tree(p)==-1| tree(p)==-2)

95 return;

96 else

49

97 inorder(tree ,2*p);

98 printf(”%d\ t ”,tree(p));99 inorder(tree ,2*p+1);

100 end

101 endfunction

102 function []= preorder(tree ,p)

103 if(tree(p)==-1| tree(p)==-2)

104 return;

105 else

106 printf(”%d\ t ”,tree(p));107 preorder(tree ,2*p);

108 preorder(tree ,2*p+1);

109 end

110 endfunction

111 function []= postorder(tree ,p)

112 if(tree(p)==-1| tree(p)==-2)

113 return;

114 else

115 postorder(tree ,2*p);

116 postorder(tree ,2*p+1);

117 printf(”%d\ t ”,tree(p));118 end

119 endfunction

120 // Ca l l i n g Rout ine :121 tree=maketree (3);

122 tree=setleft(tree ,3,1);

123 tree=setright(tree ,3,2);

124 tree=setleft(tree ,2,4);

125 tree=setright(tree ,2,5);

126 disp(” I n o r d e r t r a v e r s a l ”);127 inorder(tree ,1);

128 disp(” Preo rde r t r a v e r s a l ”);129 preorder(tree ,1);

130 disp(” Po s t o rd e r t r a v e r s a l ”);131 postorder(tree ,1);

50

Scilab code Exa 5.3 example

1 funcprot (0);

2 function[tree]= maketree(x)

3 tree=zeros (1,30);

4 for i=1:30

5 tree(i)=-1;

6 end

7 tree (1)=x;

8 tree (2)=-2;

9 endfunction

10 function[tree1 ]= setleft(tree ,tre ,x)

11 tree1 =[];

12 i=1;

13 while(tree(i)~=-2)

14 if(tree(i)==tre)

15 j=i;

16 end

17 i=i+1;

18 end

19 if(i>2*j)

20 tree (2*j)=x;

21 else

22 tree (2*j)=x;

23 tree (2*j+1)=-2;

24 for l=i:2*j-1

25 tree(i)=-1;

26 end

27 end

28 tree1=tree;

29 endfunction

30 function[tree1 ]= setright(tree ,tre ,x)

31 tree1 =[];

32 i=1;

51

33 while(tree(i)~=-2)

34 if(tree(i)==tre)

35 j=i;

36 end

37 i=i+1;

38 end

39 if(i>2*j+1)

40 tree (2*j+1)=x;

41 else

42 tree (2*j+1)=x;

43 tree (2*j+2)=-2;

44 for l=i:2*j

45 tree(i)=-1;

46 end

47 end

48 tree1=tree;

49 endfunction

50 function[x]= isleft(tree ,tre)

51 i=1;

52 x=0;

53 while(tree(i)~=-2)

54 if(tree(i)==tre)

55 j=i;

56 end

57 i=i+1;

58 end

59 if(i>=2*j)

60 if((tree (2*j)~=-1)|(tree (2*j)~=-2))

61 x=1;

62 return 1;

63 else

64 return 0;

65 end

66 else

67 x=0;

68 return x;

69 end

70 endfunction

52

71 function[x]= isright(tree ,tre)

72 i=1;

73 x=0;

74 while(tree(i)~=-2)

75 if(tree(i)==tre)

76 j=i;

77 end

78 i=i+1;

79 end

80 if(i>=2*j+1)

81 if((tree (2*j+1)~=-1)|(tree (2*j+1)~=-2))

82 x=1;

83 return 1;

84 else

85 return 0;

86 end

87 else

88 x=0;

89 return x;

90 end

91 endfunction

92 funcprot (0);

93 function []= inorder(tree ,p)

94 if(tree(p)==-1| tree(p)==-2)

95 return;

96 else

97 inorder(tree ,2*p);

98 disp(tree(p),” ”);99 inorder(tree ,2*p+1);

100 end

101 endfunction

102 function []= preorder(tree ,p)

103 if(tree(p)==-1| tree(p)==-2)

104 return;

105 else

106 disp(tree(p),” ”);107 preorder(tree ,2*p);

108 preorder(tree ,2*p+1);

53

109 end

110 endfunction

111 function []= postorder(tree ,p)

112 if(tree(p)==-1| tree(p)==-2)

113 return;

114 else

115 postorder(tree ,2*p);

116 postorder(tree ,2*p+1);

117 disp(tree(p),” ”);118 end

119 endfunction

120 function[tree1 ]= binary(tree ,x)

121 p=1;

122 while(tree(p)~=-1& tree(p)~=-2)

123 q=p;

124 if(tree(p)>x)

125 p=2*p;

126 else

127 p=2*p+1;

128 end

129 end

130 i=1;

131 while(tree(i)~=-2)

132 i=i+1;

133 end

134 if(tree(q)>x)

135 if(i==2*q)

136 tree (2*q)=x;

137 tree (2*q+1)=-2

138 else

139 if(i<2*q)

140 tree(i)=-1;

141 tree (2*q+1)=-2;

142 tree (2*q)=x;

143 end

144 end

145146 else

54

147 if(i==2*q+1)

148 tree (2*q+1)=x;

149 tree (2*q+2)=-2;

150 else

151 if(i<2*q+1)

152 tree(i)=-1;

153 tree (2*q+1)=x;

154 tree (2*q+2)=-2;

155 end

156 end

157158 end

159 tree1=tree;

160 endfunction

161 // Ca l l i n g Rout ine :162 tree=maketree (3);

163 tree=binary(tree ,1);

164 tree=binary(tree ,2);

165 tree=binary(tree ,4);

166 tree=binary(tree ,5);

167 disp(tree ,” Binary t r e e thus ob t a i n e by i n s e r t i n g1 , 2 , 4 and5 i n t r e e r o o t ed 3 i s : ”);

Scilab code Exa 5.4 example

1 function[tree1 ]= binary(tree ,x)

2 p=1;

3 while(tree(p)~=-1& tree(p)~=-2)

4 q=p;

5 if(tree(p)>x)

6 p=2*p;

7 else

8 p=2*p+1;

9 end

10 end

55

11 if(tree(q)>x)

12 if(tree (2*q)==-2)

13 tree (2*q)=x;

14 tree (2*q+1)=-2;

15 else

16 tree (2*q)=x;

17 end

18 else

19 if(tree (2*q+1)==-2)

20 tree (2*q+1)=x;

21 tree (2*q+2)=-2;

22 else

23 tree (2*q+1)=x;

24 end

25 end

26 tree1=tree;

27 endfunction

28 funcprot (0);

29 function[tree]= maketree(x)

30 tree=zeros (40 ,1);

31 for i=1:40

32 tree(i)=-1;

33 end

34 tree (1)=x;

35 tree (2)=-2;

36 endfunction

37 function []= duplicate1(a,n)

38 tree=maketree(a(1));

39 q=1;

40 p=1;

41 i=2;

42 x=a(i)

43 while(i<n)

44 while(tree(p)~=x&tree(q)~=-1& tree(q)~=-2)

45 p=q;

46 if(tree(p)<x)

47 q=2*p;

48 else

56

49 q=2*p+1;

50 end

51 end

52 if(tree(p)==x)

53 disp(x,” Dup l i c a t e ”);54 else

55 tree=binary(tree ,x);

56 end

57 i=i+1;

58 x=a(i);

59 end

60 while(tree(p)~=x&tree(q)~=-1& tree(q)~=-2)

61 p=q;

62 if(tree(p)<x)

63 q=2*p;

64 else

65 q=2*p+1;

66 end

67 end

68 if(tree(p)==x)

69 disp(x,” Dup l i c a t e ”);70 else

71 tree=binary(tree ,x);

72 end

73 endfunction

74 // Ca l l i n g Adress :75 a=[22 11 33 22 211 334]

76 duplicate1(a,6)

77 a=[21 11 33 22 22 334]

78 duplicate1(a,6)

57

Chapter 6

Graphs

Scilab code Exa 6.1 example

1 clear all;

2 clc;

3 disp(”Example 6 . 1 ”);4 //Depth F i r s t Search T r av e r s a l5 funcprot (0)

6 function []= Dfs(adj ,n);

7 i=1,j=1;

8 colour =[];

9 for i=1:n

10 for j=1:n

11 colour =[ colour (:,:) 0];

12 end

13 end

14 disp(”The DFS t r a v e r s a l i s ”);15 dfs(adj ,colour ,1,n);

16 endfunction

17 function []= dfs(adj ,colour ,r,n)

18 colour(r)=1;

19 disp(r,” ”);20 for i=1:n

21 if(adj((r-1)*n+i)&( colour(i)==0))

58

22 dfs(adj ,colour ,i,n);

23 end

24 end

25 colour(r)=2;

26 endfunction

27 // Ca l l i n g Rout ine :28 n=4;

29 adj =[0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0]

30 Dfs(adj ,n)

Scilab code Exa 6.2 example

1 clear all;

2 clc;

3 disp(”Example 6 . 2 ”);4 // //BFS Trav e r s a l5 funcprot (0)

6 function[q2]=push(ele ,q1)

7 if(q1.rear==q1.front)

8 q1.a=ele;

9 q1.rear=q1.rear +1;

10 else

11 q1.a=[q1.a(:,:) ele];

12 q1.rear=q1.rear +1;

13 end

14 q2=q1;

15 endfunction

16 function[ele ,q2]=pop(q1)

17 ele=-1;

18 q2=0;

19 if(q1.rear==q1.front)

20 return;

21 else

22 ele=q1.a(q1.rear -q1.front);

23 q1.front=q1.front +1;

59

24 i=1;

25 a=q1.a(1);

26 for i=2:(q1.rear -q1.front)

27 a=[a(:,:) q1.a(i)];

28 end

29 q1.a=a;

30 end

31 q2=q1;

32 endfunction

3334 function []= Bfs(adj ,n);

35 i=1,j=1;

36 colour =[];

37 for i=1:n

38 for j=1:n

39 colour =[ colour (:,:) 0];

40 end

41 end

42 disp(”The BFS Trav e r s a l i s ”);43 bfs(adj ,colour ,1,n);

44 endfunction

45 function []= bfs(adj ,colour ,s,n)

46 colour(s)=1;

47 q=struct( ’ r e a r ’ ,0, ’ f r o n t ’ ,0, ’ a ’ ,0);48 q=push(s,q);

49 while((q.rear) -(q.front) >0)

50 [u,q]=pop(q);

51 disp(u,” ”);52 for i=1:n

53 if(adj((u-1)*n+i)&( colour(i)==0))

54 colour(i)=1;

55 q=push(i,q);

56 end

57 end

58 colour(u)=2;

59 end

60 endfunction

61 // Ca l l i n g Rout ine :

60

62 n=4;

63 adj =[0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0]

64 Bfs(adj ,n)

Scilab code Exa 6.3 example

1 clear all;

2 clc;

3 disp(”Example 6 . 3 ”);4 // Warshal l ’ s Algor i thm5 clc;

6 clear all;

7 funcprot (0)

8 function[path]= transclose(adj ,n)

9 for i=1:n

10 for j=1:n

11 path((i-1)*n+j)=adj((i-1)*n+j);

12 end

13 end

14 for k=1:n

15 for i=1:n

16 if(path((i-1)*n+k)==1)

17 for j=1:n

18 path((i-1)*n+j)=path((i-1)*n+j)|path((k-1)

*n+j);

19 end

20 end

21 end

22 end

23 printf(” T r a n s i t i v e c l o s u r e f o r the g i v en graph i s: \ n”);

24 for i=1:n

25 printf(”For v e r t e x %d \n”,i);26 for j=1:n

27 printf(”%d %d i s %d\n”,i,j,path((i-1)*n+j));

61

28 end

29 end

30 endfunction

31 // Ca l l i n g Rout ine :32 n=3;

33 adj =[0 1 0 0 0 1 0 0 0]

34 path=transclose(adj ,n)

Scilab code Exa 6.4 example

1 clear all;

2 clc;

3 disp(”Example 6 . 4 ”);4 // Finnd ing T r a n s i t i v e C l o su r e5 funcprot (0);

6 function[path]= Tranclose(adj ,n);

7 i=1,j=1;

8 path=zeros(n*n,1);

9 path=tranclose(adj ,n);

10 printf(” T r a n s i t i v e C l o su r e Of Given Graph i s : \ n”);11 for i=1:n

12 printf(”For Vertex %d\n”,i);13 for j=1:n

14 printf(” %d %d i s %d\n”,i,j,path((i-1)*n+j));15 end

16 end

1718 endfunction

19 function[path]= tranclose(adj ,n)

20 adjprod=zeros(n*n,1);

21 k=1;

22 newprod=zeros(n*n,1);

23 for i=1:n

24 for j=1:n

25 path((i-1)*n+j)=adj((i-1)*n+j);

62

26 adjprod ((i-1)*n+j)= path((i-1)*n+j);

27 end

28 end

29 for i=1:n

30 newprod=prod1(adjprod ,adj ,n);

31 for j=1:n

32 for k=1:n

33 path((j-1)*n+k)=path((j-1)*n+k)|newprod ((j

-1)*n+k);

34 end

35 end

36 for j=1:n

37 for k=1:n

38 adjprod ((j-1)*n+k)=newprod ((j-1)*n+k);

39 end

40 end

41 end

42 endfunction

43 function[c]=prod1(a,b,n)

44 for i=1:n

45 for j=1:n

46 val=0

47 for k=1:n

48 val=val|(a((i-1)*n+k)&b((k-1)*n+j));

49 end

50 c((i-1)*n+j)=val;

51 end

52 end

53 endfunction

54 // Ca l l i n g Rout ine :55 n=3;

56 adj =[0 1 0 0 0 1 0 0 0]

57 path=Tranclose(adj ,n)

Scilab code Exa 6.5 example

63

1 clear all;

2 clc;

3 disp(”Example 6 . 5 ”);4 // F ind ing The Number Of S imple Paths From One Po int

To Another In A Given Graph5 funcprot (0)

6 function []= sim_path(n,adj ,i,j);

7 l=0;

8 m=1;

9 for m=1:n

10 l=l+path(m,n,adj ,i,j);

11 end

12 printf(”There a r e %d s imp l e paths from %d to %din the g i v en graph \n”,l,i,j);

13 endfunction

14 function[b]=path(k,n,adj ,i,j)

15 b=0;

16 if(k==1)

17 b=adj((i-1)*n+j);

18 else

19 for c=1:n

20 if(adj((i-1)*n+c)==1)

21 b=b+path(k-1,n,adj ,c,j);

22 end

23 end

24 end

25 return b;

26 endfunction

27 n=3;

28 adj =[0 1 1 0 0 1 0 0 0];

29 b=sim_path(n,adj ,1,3)

Scilab code Exa 6.6 example

1 clear all;

64

2 clc;

3 disp(”Example 6 . 6 ”);4 // D i j k s t r a s Algor i thm5 funcprot (0)

6 function[l]=short(adj ,w,i1 ,j1,n)

7 for i=1:n

8 for j=1:n

9 if(w((i-1)*n+j)==0)

10 w((i-1)*n+j)=9999;

11 end

12 end

13 end

1415 distance =[];

16 perm =[];

17 for i=1:n

18 distance =[ distance (:,:) 99999];

19 perm=[perm (:,:) 0];

20 end

21 perm(i1)=1;

22 distance(i1)=0;

23 current=i1;

24 while(current ~=j1)

25 smalldist =9999;

26 dc=distance(current);

27 for i=1:n

28 if(perm(i)==0)

29 newdist=dc+w((current -1)*n+i);

30 if(newdist <distance(i))

31 distance(i)=newdist;

32 end

33 if(distance(i)<smalldist)

34 smalldist=distance(i);

35 k=i;

36 end

37 end

38 end

39 current=k;

65

40 perm(current)=1;

41 end

42 l=distance(j1);

43 printf(”The s h o r t e s t path between %d and %d i s %d”,i1 ,j1,l);

44 endfunction

45 // Ca l l i n g Rout ine :46 n=3;

47 adj =[0 1 1 0 0 1 0 0 0] // Adjacency L i s t48 w=[0 12 22 0 0 9 0 0 0] // we ight l i s t f i l l 0 f o r no

edge49 short(adj ,w,1,3,n);

Scilab code Exa 6.7 example

1 clear all;

2 clc;

3 disp(”Example 6 . 7 ”);4 // F ind ing The Number Of Paths From One Vertex To

Another Of A Given Length56 function[b]=path(k,n,adj ,i,j)

7 b=0;

8 if(k==1)

9 b=adj((i-1)*n+j);

10 else

11 for c=1:n

12 if(adj((i-1)*n+c)==1)

13 b=b+path(k-1,n,adj ,c,j);

14 end

15 end

16 end

17 printf(”Number o f paths from ve r t e x %d to %d o fl e n g t h %d ar e %d”,i,j,k,b);

18 return b;

66

19 endfunction

20 // Ca l l i n g Rout ine :21 n=3;

22 adj =[0 1 1 0 0 1 0 0 0]

23 b=path(1,n,adj ,1,3)

67

Chapter 7

Sorting

Scilab code Exa 7.1 example

1 clear all;

2 clc;

3 disp(”Example 7 . 1 ”);4 funcprot (0);

5 function[a1]= insertion(a,n)

6 for k=1:n

7 y=a(k);

8 i=k;

9 while(i>=1)

10 if(y<a(i))

11 a(i+1)=a(i);

12 a(i)=y;

13 end

14 i=i-1;

15 end

16 end

17 a1=a;

18 disp(a1,” So r t ed a r r ay i s : ”);19 endfunction

20 // Ca l l i n g Rout ine :21 a=[5 4 3 2 1] // worst−c a s e behav i ou r o f

68

i n s e r t i o n s o r t .22 disp(a,”Given Array ”);23 a1=insertion(a,5)

Scilab code Exa 7.2 example

1 clear all;

2 clc;

3 disp(”Example 7 . 2 ”);4 funcprot (0);

5 function[a1]= insertion(a,n)

6 for k=1:n

7 y=a(k);

8 i=k;

9 while(i>=1)

10 if(y<a(i))

11 a(i+1)=a(i);

12 a(i)=y;

13 end

14 i=i-1;

15 end

16 end

17 a1=a;

18 disp(a1,” So r t ed a r r ay i s : ”);19 endfunction

20 // Ca l l i n g Rout ine :21 a=[2 3 4 5 1]

22 disp(a,”Given Array ”);23 a1=insertion(a,5)

Scilab code Exa 7.3 example

1 clear all;

69

2 clc;

3 disp(”Example 7 . 3 ”);4 funcprot (0);

5 function[a1]=quick(a);

6 a=gsort(a);// IN BUILT QUICK SORT FUNCTION7 n=length(a);

8 a1=[];

9 for i=1:n

10 a1=[a1(:,:) a(n+1-i)];

11 end

12 disp(a1,” So r t ed a r r ay i s : ”);13 endfunction

14 // Ca l l i n g Rout ine :15 a=[26 5 37 1 61 11 59 15 48 19]

16 disp(a,”Given Array ”);17 a1=quick(a)

Scilab code Exa 7.4 example

1 clear all;

2 clc;

3 disp(”Example 7 . 4 ”);4 function[a1]= insertion(a,n)

5 for k=1:n

6 y=a(k);

7 i=k;

8 while(i>=1)

9 if(y<a(i))

10 a(i+1)=a(i);

11 a(i)=y;

12 end

13 i=i-1;

14 end

15 end

16 a1=a;

70

17 disp(a1,” So r t ed a r r ay i s : ”);18 endfunction

19 // Ca l l i n g Rout ine :20 a=[3 1 2]

21 disp(a,”Given Array ”);22 a1=insertion(a,3)

Scilab code Exa 7.5 example

1 clear all;

2 clc;

3 disp(”Example 7 . 5 ”);4 funcprot (0);

5 function[a1]= mergesort(a,p,r)

6 if(p<r)

7 q=int((p+r)/2);

8 a=mergesort(a,p,q);

9 a=mergesort(a,q+1,r);

10 a=merge(a,p,q,r);

11 else

12 a1=a;

13 return;

14 end

15 a1=a;

16 endfunction

17 function[a1]=merge(a,p,q,r)

18 n1=q-p+1;

19 n2=r-q;

20 left=zeros(n1+1);

21 right=zeros(n2+1);

22 for i=1:n1

23 left(i)=a(p+i-1);

24 end

25 for i1=1:n2

26 right(i1)=a(q+i1);

71

27 end

28 left(n1+1) =999999999;

29 right(n2+1) =999999999;

30 i=1;

31 j=1;

32 k=p;

33 for k=p:r

34 if(left(i)<=right(j))

35 a(k)=left(i);

36 i=i+1;

37 else

38 a(k)=right(j);

39 j=j+1;

40 end

41 end

42 a1=a;

43 endfunction

44 // Ca l l i n g Rout ine :45 a=[26 5 77 1 61 11 59 15 48 19]

46 disp(a,”Given Array ”);47 a1=mergesort(a,1 ,10)

48 disp(a1,” So r t ed a r r ay i s : ”);

Scilab code Exa 7.6 example

1 clear all;

2 clc;

3 disp(”Example 7 . 7 ”);4 function[a1]=shell(a,n,incr ,nic)

5 for i=1: nic

6 span=incr(i);

7 for j=span +1:n

8 y=a(j);

9 k=j-span;

10 while(k>=1&y<a(k))

72

11 a(k+span)=a(k);

12 k=k-span;

13 end

14 a(k+span)=y;

15 end

16 end

17 a1=a;

18 disp(a1,” So r t ed a r r ay i s : ”);19 endfunction

20 // Ca l l i n g Rout ine :21 a=[23 21 232 121 2324 1222433 1212]

22 disp(a,”Given Array ”);23 incr =[5 3 1] //must a lways end with 124 a1=shell(a,7,incr ,3)

Scilab code Exa 7.7 example

1 clear all;

2 clc;

3 disp(”Example 7 . 7 ”);4 function[a1]=shell(a,n,incr ,nic)

5 for i=1: nic

6 span=incr(i);

7 for j=span +1:n

8 y=a(j);

9 k=j-span;

10 while(k>=1&y<a(k))

11 a(k+span)=a(k);

12 k=k-span;

13 end

14 a(k+span)=y;

15 end

16 end

17 a1=a;

18 disp(a1,” So r t ed a r r ay i s : ”);

73

19 endfunction

20 // Ca l l i n g Rout ine :21 a=[23 21 232 121 2324 1222433 1212]

22 disp(a,”Given Array ”);23 incr =[5 3 1] //must a lways end with 124 a1=shell(a,7,incr ,3)

Scilab code Exa 7.8 example

1 clear all;

2 clc;

3 function []= sortedsearch(a,n,ele)

4 if(a(1)>ele|a(n)<ele)

5 disp(”NOT IN THE LIST”);6 else

7 i=1;

8 j=0;

9 for i=1:n

10 if(a(i)==ele)

11 printf(”FOUND %d AT %d”,ele ,i);12 j=1;

13 else

14 if(a(i)>ele)

15 break;

16 end

17 end

18 end

19 if(j==0)

20 disp(”%d NOT FOUND”,ele);21 end

22 end

23 endfunction

24 // Ca l l i n g Rout ine :25 a=[2 22 23 33 121 222 233] // a shou ld be s o r t e d26 disp(a,”Given a r r ay ”);

74

27 sortedsearch(a,7,23)

75

Chapter 8

Hashing

Scilab code Exa 8.1 example

1 clear all;

2 clc;

3 disp(”Example 8 . 1 ”);4 k=12320324111220;

5 p1=123;

6 p2=203;

7 p3 =241;...... // key k p a r t i t i o n e d i n t o p a r t s tha t a r e3 dec ima l l ong .

8 p4=112;

9 p5=20;

10 // / . . . . . u s i n g s h i f t f o l d i n g . . .11 // . . . . p a r t i t i o n s a r e added to ge t the hash add r e s s .12 z=p1+p2+p3+p4+p5;

13 disp(z);

14 //when f o l d i n g at the bounda r i e s i s used , we r e v e r s ep2 and p4 .

15 p2=302;

16 p4=211;

17 x=p1+p2+p3+p4+p5;

18 disp(x);

76

Scilab code Exa 8.2 example

1 clear all;

2 clc;

3 disp(”Example 8 . 2 ”);4 function []= stringtoint ()

5 num= ascii(” s c i l a b ”);6 disp(” d i s p l a y i n a s c i i c ode s o f a l phab e t s=”);7 disp(num);

8 // c onv e r t i n g s t r i n g s i n t o un ique non−n e g a t i v ei n t e g e r and suming t h e s e un ique i n t e g e r s .

9 z=sum(num);

10 disp(” d i s p l a y i n sum o f t h e s e i n t e g e r s ”);11 disp(z);

12 endfunction

13 stringtoint ()

77

Chapter 9

Priority Queues

Scilab code Exa 9.1 example

1 clear all;

2 clc;

3 // Implement ing P r i o r i t y Queue Using L i s t s4 funcprot (0)

5 function[link2 ]= insert_pri(ele ,link1)

6 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

7 if(link1 (1) (1).add ==0)

8 link1 (1) (1).data=ele;

9 link1 (1) (1).add=1;

10 link1 (1) (1).nexadd =1;

11 link2 (1)=link1 (1) (1);

12 else

13 if(link1 (1) (1).nexadd ==link1 (1) (1).add)

14 if(ele >=link1 (1)(1).data)

15 t=ele;

16 p=link1 (1) (1).data;

17 else

18 t=link1 (1) (1).data;

19 p=ele;

78

20 end

21 link1 (1) (1).data=t;

22 lin2=link1 (1) (1);

23 lin2.data=p;

24 lin2.add=2;

25 lin2.nexadd=link1 (1)(1).add;

26 link1 (1) (1).nexadd=lin2.add;

27 link2 (1)=link1 (1) (1);

28 link2 (2)=lin2;

29 else

30 i=1;

31 a=[];

32 while(link1(i).nexadd ~= link1 (1)(1).add)

33 a=[a(:,:) link1(i).data];

34 i=i+1;

35 end

36 a=[a(:,:) link1(i).data];

37 a=gsort(a);

38 j=1;

39 while(j<=i)

40 link1(j).data=a(j);

41 j=j+1;

42 end

43 k=1;

44 while(link1(k).data >=ele)

45 if(link1(k).nexadd ==link1 (1)(1).add)

46 break;

47 else

48 link2(k)=link1(k);

49 k=k+1;

50 end

51 end

52 if(link1(k).nexadd ~=link1 (1)(1).add)

53 lin2=link1(k);

54 lin2.data=ele;

55 lin2.add=link1(k).add;

56 j=k;

57 y=link1 (1) (1).add;

79

58 while(link1(k).nexadd ~=y)

59 link1(k).add=link1(k).add+1;

60 link1(k).nexadd=link1(k).nexadd +1;

61 k=k+1;

62 end

63 link1(k).add=link1(k).add+1;

64 lin2.nexadd=link1(j).add;

65 link2(j)=lin2;

66 j=j+1;

67 while(j<=k+1)

68 link2(j)=link1(j-1);

69 j=j+1;

70 end

71 else

72 lin2=link1(k);

73 lin2.data=ele;

74 lin2.nexadd=link1 (1)(1).add;

75 lin2.add=link1(k).add+1;

76 link1(k).nexadd=lin2.add;

77 j=1;

78 while(j<=k)

79 link2(j)=link1(j);

80 j=j+1;

81 end

82 link2(j)=lin2;

83 end

84 end

85 end

86 endfunction

87 function[ele ,link2]= extract_min(link1);

88 link2=list

(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,,0,0)

;

89 i=1;

90 ele=-1;

91 if(link1 (1) (1).add ==0)

92 disp(” Under f low ”);93 return;

80

94 else

95 if(link1 (1)(1).nexadd ==link1 (1) (1).add)

96 link1 (1) (1).add=0;

97 link1 (1) (1).nexadd =0;

98 ele=link1 (1) (1).data;

99 link1 (1) (1).data =0;

100 link2 (1)=link1 (1) (1);

101 else

102 i=1;

103 while(link1(i).nexadd ~= link1 (1) (1).add)

104 link2(i)=link1(i);

105 i=i+1;

106 end

107 ele=link1(i).data;

108 link2(i-1).nexadd=link2 (1).add;

109 end

110 end

111 endfunction

112 // Ca l l i n g Rout ine :113 link1=struct( ’ data ’ ,0, ’ add ’ ,0, ’ nexadd ’ ,0);114 link1=insert_pri (3,link1);

115 link1=insert_pri (4,link1);

116 link1=insert_pri (22,link1);

117 link1=insert_pri (21,link1);

118 link1=insert_pri (11,link1);

119 disp(link1 ,” L i s t A f t e r I n s e r t i o n s ”);120 [ele ,link1]= extract_min(link1)

121 disp(ele ,”Element a f t e r the min e x t r a c t i o n ”);

81